Table of contents
Is there a Difference? How to use ANOVA to Find Out
The An analysis tool in statistics called Analysis of Variance (... Learn More... F ratio example is the ratio of two mean square values. If the Hypothesis testing definition A statistical hypothesis test ... Learn More... is true, you expect F to have a value close to 1.0. A large F ratio means that the variation among group means is more than you’d expect to see by chance.
Below is an example of how to calculate the F-Statistic for an ANOVA (An analysis tool in statistics called Analysis of Variance (... Learn More...):
A company produces bags of popped popcorn. The customer’s “Critical to Quality (CTQ) in Six Sigma, Trees can help to un... Learn More... Requirement” is to have the least number of un-popped kernels in a bag. We are going to take data from three vendors to determine if there is a difference in the number of un-popped popcorn kernels between the vendors.
A The Six Sigma Green Belt is a certificate that professionals... Learn More... and his team are going to run a Hypothesis testing definition A statistical hypothesis test ... Learn More... with the following settings:
- 1 Statistics can be confusing as the term "factor" can have di... Learn More... or Variable (which is the type of Kernel)
- 3 Settings (which in this case are 3 different vendors)
- N = The sample size is an important feature of any empirical stu... Learn More... of 25 for each vendor (for a total of 75 samples)
Degrees of Freedom (this is the statistical bank account that we have to contribute to)
- Degrees of Freedom of the Factor (Type of Kernel) = 3 Vendors – 1 (=2)
- Total Degrees of Freedom = Sample Size of 25 – 1 (=24)
- Degrees of Freedom of Statistics error The dual dimension of error statistics is p... Learn More... (or Unexplained) = DF Total – DF Factor (=22)
Degrees of Freedom for the Factor (2)/ Degrees of Freedom for the Unexplained (or Error) (22)= Critical F-Statistic (2/22)
Look this up in this table: (https://www.statsoft.com/textbook/distribution-tables/#f05)
If you look up a table of F-Values (we are going to say that we will test this at the significance Statistics level A statistics level is the value of input in... Learn More... of 0.05 (at 95% Confidence), so, therefore, we are willing to take only a 5% risk of being wrong) you will find that the:
If the Calculated F-Value is less than the Critical F-Statistic of 3.44, then we “Accept the A statistical hypothesis is a hypothesis that is testabl... Learn More....”
- Null Hypothesis (H0): “There is no difference in the number of un-popped kernels between vendors”
- An alternative hypothesis (Ha) states that there is a s... Learn More...: “There is a difference in the number of un-popped kernels between vendors”
- Alpha is 0.05
Note* The F A Sample Statistic, and a Population Parameter A sample for... Learn More... must be used in combination with the P value when you are deciding if your overall results are significant. If you have a significant F Statistic, it doesn’t mean that all variables are significant. The F-Statistic might be indicating that one is different. There might not be enough difference to cause the Statistical Validity of the test to be questioned.
Here is a resource for the Table with the Critical F-Statistic Values: